| Title:
|
On measurable solutions of a functional equation and their application to information theory (English) |
| Author:
|
Dial, Gur |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1983 |
| Pages:
|
103-107 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon's entropy and entropy of type $\beta$ is given. (English) |
| Keyword:
|
measurable solutions |
| Keyword:
|
system |
| Keyword:
|
Shannon’s entropy |
| MSC:
|
39B30 |
| MSC:
|
39B99 |
| MSC:
|
94A15 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 0513.39006 |
| idMR:
|
MR0695183 |
| DOI:
|
10.21136/AM.1983.104010 |
| . |
| Date available:
|
2008-05-20T18:21:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104010 |
| . |
| Reference:
|
[1] J. Aczel: Lectures on functional equations and their applications.Academic Press, New York, 1966. Zbl 0139.09301, MR 0208210 |
| Reference:
|
[2] J. Aczel Z. Daroczy: On measures of information and their characterizations.Academic Press, New York, 1975. MR 0689178 |
| Reference:
|
[3] Z. Daroczy, Losonczi: Über die Erweiterung der auf einer Punktmenge additive Funktion.Publ Math. Debrecen, 14 (1967) 239-245. MR 0240492 |
| Reference:
|
[4] I. J. Taneja: A joint characterization of Shannons entropy of type through a functional equation.Journal of Mathematical Sciences, (10, 1975), 69-74. MR 0539497 |
| . |
